Explanation Given information: The cost of producing q units of a good is C ( q ) = 0.1 q 2 + 1000 million dollars. Concept Used: Fixed cost: The Fixed Cost (FC) is the amount of money spent regardless of number of items produced. FC can include things like rent, purchase costs of machinery, and salaries for office staff. If the cost of producing a quantity q is C ( q ) , then the fixed cost, is given by C ( 0 ) . Average cost: Average cost is the slope of the line from the origin to a point on the cost curve. The average cost is the cost per unit of producing a certain quantity; it is the total cost divided by the number of units produced. If the cost of producing a quantity q is C ( q ) , then the average cost, a ( q ) , of producing a quantity q is given by a ( q ) = C ( q ) q . Marginal cost: If you can model your cost as a function of quantity, the derivative of that is the marginal cost. It's the rate at which costs are increasing for that incremental unit. If the cost of producing a quantity q is C ( q ) , then the marginal cost, M ( q ) , of producing a quantity q is given by M ( q ) = C ' ( q ) . Calculation: Steps Description C ( 0 ) = 0 To determine (b) To find: The production level at which the average cost have a critical point. To determine (c) To find: Whether the critical point a local maximum or a local minimum or neither.

Applied Calculus, 6e WileyPLUS + Loose-leaf

6th Edition

ISBN: 9781119408901

Author: Deborah Hughes-Hallett, Andrew M. Gleason, Patti Frazer Lock, Daniel E. Flath

Publisher: Wiley (WileyPLUS Products)

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Question

Chapter 4.5, Problem 7P

To determine

(a)

To find:

The fixed cost, marginal cost and the average cost.

To determine

(b)

To find:

The production level at which the average cost have a critical point.

To determine

(c)

To find:

Whether the critical point a local maximum or a local minimum or neither.

Expert Solution & Answer

Chapter 4 Solutions

Applied Calculus, 6e WileyPLUS + Loose-leaf

Ch. 4.1 - Prob. 1P Ch. 4.1 - Prob. 2P Ch. 4.1 - Prob. 3P Ch. 4.1 - Prob. 4P Ch. 4.1 - Prob. 5P Ch. 4.1 - Prob. 6P Ch. 4.1 - Prob. 7P Ch. 4.1 - Prob. 8P Ch. 4.1 - Prob. 9P Ch. 4.1 - Prob. 10P

Ch. 4.1 - Prob. 11P Ch. 4.1 - Prob. 12P Ch. 4.1 - Prob. 13P Ch. 4.1 - Prob. 14P Ch. 4.1 - Prob. 15P Ch. 4.1 - Prob. 16P Ch. 4.1 - Prob. 17P Ch. 4.1 - Prob. 18P Ch. 4.1 - Prob. 19P Ch. 4.1 - Prob. 20P Ch. 4.1 - Prob. 21P Ch. 4.1 - Prob. 22P Ch. 4.1 - Prob. 23P Ch. 4.1 - Prob. 24P Ch. 4.1 - Prob. 25P Ch. 4.1 - Prob. 26P Ch. 4.1 - Prob. 27P Ch. 4.1 - Prob. 28P Ch. 4.1 - Prob. 29P Ch. 4.1 - Prob. 30P Ch. 4.1 - Prob. 31P Ch. 4.1 - Prob. 32P Ch. 4.1 - Prob. 33P Ch. 4.1 - Prob. 34P Ch. 4.1 - Prob. 35P Ch. 4.1 - Prob. 36P Ch. 4.1 - Prob. 37P Ch. 4.1 - Prob. 38P Ch. 4.1 - Prob. 39P Ch. 4.1 - Prob. 40P Ch. 4.1 - Prob. 41P Ch. 4.1 - Prob. 42P Ch. 4.1 - Prob. 43P Ch. 4.1 - Prob. 44P Ch. 4.1 - Prob. 45P Ch. 4.1 - Prob. 46P Ch. 4.1 - Prob. 47P Ch. 4.1 - Prob. 48P Ch. 4.1 - Prob. 49P Ch. 4.1 - Prob. 50P Ch. 4.1 - Prob. 51P Ch. 4.1 - Prob. 52P Ch. 4.1 - Prob. 53P Ch. 4.1 - Prob. 54P Ch. 4.1 - Prob. 55P Ch. 4.1 - Prob. 56P Ch. 4.1 - Prob. 57P Ch. 4.1 - Prob. 58P Ch. 4.2 - Prob. 1P Ch. 4.2 - Prob. 2P Ch. 4.2 - 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(a) To find: The fixed cost, marginal cost and the average cost.

Solution Summary: The author explains the fixed cost, marginal cost and average cost.

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(a) To find: The fixed cost, marginal cost and the average cost.

(b) To find: The production level at which the average cost have a critical point.

(c) To find: Whether the critical point a local maximum or a local minimum or neither.

Chapter 4 Solutions

(a)

To find:

The fixed cost, marginal cost and the average cost.

(b)

To find:

The production level at which the average cost have a critical point.

(c)

To find:

Whether the critical point a local maximum or a local minimum or neither.